The purpose of this study is to illustrate the use of explanatory models based on Rasch measurement theory to detect systematic relationships between student and item characteristics and achievement differences using differential item functioning (DIF), differential group functioning (DGF), and differential person functioning (DPF) techniques. The major focus of the analyses in this study was to demonstrate a set of methodological techniques that can be used to better understand subgroup performance on a large-scale writing assessment, rather than to conduct bias or sensitivity reviews. Tables and figures are appended.